Masks have been used for skin clarification for thousands of years. In essence, you put a layer of 'sticky stuff' on your face, whether it's clay, gel, or other combinations. Because it has a bit of stickiness to it, and is mostly liquid goo, it squishes down into your nooks, crannies and pores of your face, connecting with all the dirt and grime hiding in there. As the goo dries, it pulls away from your skin, and it pulls all of those impurities and dead skin cells with it. This is sort of like if you took tape and pressed it against a linty sweater - when you lifted the tape, all that lint would stick to the tape and lift away with it.
When you then wash off the dried up goo, you also wash away all that old oil, dirt, grime, etc that was buried deep in your pores. You wash away the dried dead skin. That leaves you with fresh, clean, non-oily skin. The masks tend to have a good amount of water in them so as they dry, your skin is being hydrated, which is a good thing. Your pores, now clean of junk, can close up and be nice and small, giving your face a smoother appearance. Your blood vessels tend to open up a bit with this warmth, which means they do a much better job of bringing nutrients to your skin and removing toxins and impurities.
So in general a face mask is VERY good for your skin - not just from a beauty standpoint (fewer acne problems, cleaner pores, smaller pores) but also from a health standpoint. Your skin is literally how your body keeps infections and virusses from entering your body, so the healthier your skin, the healthier you are.